The $$ \mathcal{N} $$ = 3 Weyl multiplet in four dimensions

Abstract The main ingredient for local superconformal methods is the multiplet of gauge fields: the Weyl multiplet. We construct the transformations of this multiplet for $$ \mathcal{N} $$ N = 3, D = 4. The construction is based on a supersymmetry truncation from the $$ \mathcal{N} $$ N = 4 Weyl multiplet, on coupling with a current multiplet, and on the implementation of a soft algebra at the nonlinear level, extending $$ \mathfrak{s}\mathfrak{u} $$ s u (2, 2|3). This is the first step towards a superconformal calculus for $$ \mathcal{N} $$ N = 3, D = 4.